# ---
# title: 1250. Check If It Is a Good Array
# id: problem1250
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Math
# link: <https://leetcode.com/problems/check-if-it-is-a-good-array/description/>
# hidden: true
# ---
# 
# Given an array `nums` of positive integers. Your task is to select some subset
# of `nums`, multiply each element by an integer and add all these numbers. The
# array is said to be  **good  **if you can obtain a sum of `1` from the array
# by any possible subset and multiplicand.
# 
# Return `True` if the array is **good  **otherwise return `False`.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: nums = [12,5,7,23]
#     Output: true
#     Explanation: Pick numbers 5 and 7.
#     5*3 + 7*(-2) = 1
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: nums = [29,6,10]
#     Output: true
#     Explanation: Pick numbers 29, 6 and 10.
#     29*1 + 6*(-3) + 10*(-1) = 1
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: nums = [3,6]
#     Output: false
#     
# 
# 
# 
# **Constraints:**
# 
#   * `1 <= nums.length <= 10^5`
#   * `1 <= nums[i] <= 10^9`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
